The center conditions and bifurcation of limit cycles at the infinity for a cubic polynomial system |
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Authors: | Lina Zhang Yirong LiuXuejiao Jiang |
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Institution: | a Center of Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, Yunnan 650093, PR China b Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, PR China c Mathematical College, Lishui University, Lishui, Zhejiang 323000, PR China |
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Abstract: | In this paper, the problem of center conditions and bifurcation of limit cycles at the infinity for a class of cubic systems are investigated. The method is based on a homeomorphic transformation of the infinity into the origin, the first 21 singular point quantities are obtained by computer algebra system Mathematica, the conditions of the origin to be a center and a 21st order fine focus are derived, respectively. Correspondingly, we construct a cubic system which can bifurcate seven limit cycles from the infinity by a small perturbation of parameters. At the end, we study the isochronous center conditions at the infinity for the cubic system. |
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Keywords: | Cubic polynomial system Infinity Singular point quantities Center Isochronous center Bifurcation of limit cycles |
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